





import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format='''%(message)s''')







def   __lowerCamelCase   (				__a  :int       )						->							np.ndarray:






		"""simple docstring"""

		return input_array.reshape((input_array.size, 1)       )







def   __lowerCamelCase   (				__a  :int       ,	__a  :Tuple       ,	__a  :int       )						->							np.ndarray:






		"""simple docstring"""

		A__     =  np.nan
		for i in range(__lowerCAmelCase       ):
				A__     =  features[:, labels == i]
				A__     =  data.mean(1       )
				# Centralize the data of class i
				A__     =  data - column_reshape(__lowerCAmelCase       )
				if i > 0:
						# If covariance_sum is not None
						covariance_sum += np.dot(__lowerCAmelCase       ,	centered_data.T       )
				else:
						# If covariance_sum is np.nan (i.e. first loop)
						A__     =  np.dot(__lowerCAmelCase       ,	centered_data.T       )

		return covariance_sum / features.shape[1]







def   __lowerCamelCase   (				__a  :Dict       ,	__a  :List[str]       ,	__a  :List[str]       )						->							np.ndarray:






		"""simple docstring"""

		A__     =  features.mean(1       )
		A__     =  np.nan
		for i in range(__lowerCAmelCase       ):
				A__     =  features[:, labels == i]
				A__     =  data.shape[1]
				A__     =  data.mean(1       )
				if i > 0:
						# If covariance_sum is not None
						covariance_sum += device_data * np.dot(
						    column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )       ,	(column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )).T       ,	)
				else:
						# If covariance_sum is np.nan (i.e. first loop)
						A__     =  device_data * np.dot(
						    column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )       ,	(column_reshape(__lowerCAmelCase       ) - column_reshape(__lowerCAmelCase       )).T       ,	)

		return covariance_sum / features.shape[1]







def   __lowerCamelCase   (				__a  :Union[str, Any]       ,	__a  :int       )						->							np.ndarray:






		"""simple docstring"""

		if features.any():
				A__     =  features.mean(1       )
				# Center the dataset
				A__     =  features - np.reshape(__lowerCAmelCase       ,	(data_mean.size, 1)       )
				A__     =  np.dot(__lowerCAmelCase       ,	centered_data.T       ) / features.shape[1]
				A__ ,     A__     =  np.linalg.eigh(__lowerCAmelCase       )
				# Take all the columns in the reverse order (-1), and then takes only the first
				A__     =  eigenvectors[:, ::-1][:, 0:dimensions]
				# Project the database on the new space
				A__     =  np.dot(filtered_eigenvectors.T       ,	__lowerCAmelCase       )
				logging.info("""Principal Component Analysis computed"""       )

				return projected_data
		else:
				logging.basicConfig(level=logging.ERROR       ,	format="""%(message)s"""       ,	force=__lowerCAmelCase       )
				logging.error("""Dataset empty"""       )
				raise AssertionError







def   __lowerCamelCase   (				__a  :Optional[int]       ,	__a  :Optional[Any]       ,	__a  :Optional[Any]       ,	__a  :Dict       )						->							np.ndarray:






		"""simple docstring"""

		assert classes > dimensions

		# Check if features have been already loaded
		if features.any:
				A__ ,     A__     =  eigh(
				    covariance_between_classes(__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       )       ,	covariance_within_classes(__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       )       ,	)
				A__     =  eigenvectors[:, ::-1][:, :dimensions]
				A__ ,     A__ ,     A__     =  np.linalg.svd(__lowerCAmelCase       )
				A__     =  svd_matrix[:, 0:dimensions]
				A__     =  np.dot(filtered_svd_matrix.T       ,	__lowerCAmelCase       )
				logging.info("""Linear Discriminant Analysis computed"""       )

				return projected_data
		else:
				logging.basicConfig(level=logging.ERROR       ,	format="""%(message)s"""       ,	force=__lowerCAmelCase       )
				logging.error("""Dataset empty"""       )
				raise AssertionError







def   __lowerCamelCase   (				)						->							None:






		"""simple docstring"""

		A__     =  np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]       )
		A__     =  np.array([0, 0, 0, 1, 1]       )
		A__     =  2
		A__     =  2

		# Assert that the function raises an AssertionError if dimensions > classes
		with pytest.raises(__lowerCAmelCase       ) as error_info:
				A__     =  linear_discriminant_analysis(
				    __lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       )
				if isinstance(__lowerCAmelCase       ,	np.ndarray       ):
						raise AssertionError(
						    """Did not raise AssertionError for dimensions > classes"""       )
				assert error_info.type is AssertionError







def   __lowerCamelCase   (				)						->							None:






		"""simple docstring"""

		A__     =  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       )
		A__     =  2
		A__     =  np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]]       )

		with pytest.raises(__lowerCAmelCase       ) as error_info:
				A__     =  principal_component_analysis(__lowerCAmelCase       ,	__lowerCAmelCase       )
				if not np.allclose(__lowerCAmelCase       ,	__lowerCAmelCase       ):
						raise AssertionError
				assert error_info.type is AssertionError


if __name__ == "__main__":
					import doctest

					doctest.testmod()




"""simple docstring"""


from __future__ import annotations

from typing import Any






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase      ,					_lowerCamelCase      ,					_lowerCamelCase = 0 ):
										lowerCamelCase__   , lowerCamelCase__   =row, column
										lowerCamelCase__   =[[default_value for c in range(_lowerCamelCase )] for r in range(_lowerCamelCase )]

				def __str__( self ):
										lowerCamelCase__   =F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

										# Make string identifier
										lowerCamelCase__   =0
										for row_vector in self.array:
																for obj in row_vector:
																						lowerCamelCase__   =max(_lowerCamelCase      ,					len(str(_lowerCamelCase ) ) )
										lowerCamelCase__   =F'''%{max_element_length}s'''

										# Make string and return
										def single_line(_lowerCamelCase ) -> str:
																nonlocal string_format_identifier
																lowerCamelCase__   ="["
																line += ", ".join(string_format_identifier % (obj,) for obj in row_vector )
																line += "]"
																return line

										s += "\n".join(single_line(_lowerCamelCase ) for row_vector in self.array )
										return s

				def __repr__( self ):
										return str(self )

				def 						_a      ( self      ,					_lowerCamelCase ):
										if not (isinstance(_lowerCamelCase      ,					(list, tuple) ) and len(_lowerCamelCase ) == 2):
																return False
										elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
																return False
										else:
																return True

				def __getitem__( self      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										return self.array[loc[0]][loc[1]]

				def __setitem__( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										lowerCamelCase__   =value

				def __add__( self      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == another.row and self.column == another.column

										# Add
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c] + another[r, c]
										return result

				def __neg__( self ):
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =-self[r, c]
										return result

				def __sub__( self      ,					_lowerCamelCase ):
										return self + (-another)

				def __mul__( self      ,					_lowerCamelCase ):

										if isinstance(_lowerCamelCase      ,					(int, float) ):  # Scalar multiplication
																lowerCamelCase__   =Matrix(self.row      ,					self.column )
																for r in range(self.row ):
																						for c in range(self.column ):
																												lowerCamelCase__   =self[r, c] * another
																return result
										elif isinstance(_lowerCamelCase      ,					_lowerCamelCase ):  # Matrix multiplication
																assert self.column == another.row
																lowerCamelCase__   =Matrix(self.row      ,					another.column )
																for r in range(self.row ):
																						for c in range(another.column ):
																												for i in range(self.column ):
																																		result[r, c] += self[r, i] * another[i, c]
																return result
										else:
																lowerCamelCase__   =F'''Unsupported type given for another ({type(_lowerCamelCase )})'''
																raise TypeError(_lowerCamelCase )

				def 						_a      ( self ):
										lowerCamelCase__   =Matrix(self.column      ,					self.row )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c]
										return result






				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase ) and isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == self.column == u.row == v.row  # u, v should be column vector
										assert u.column == v.column == 1  # u, v should be column vector

										# Calculate
										lowerCamelCase__   =v.transpose()
										lowerCamelCase__   =(v_t * self * u)[0, 0] + 1
										if numerator_factor == 0:
																return None  # It's not invertable
										return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							lowerCamelCase__   =Matrix(3  ,       3  ,       0							)
							for i in range(3							):
													lowerCamelCase__   =1
							print(F'''a^(-1) is {ainv}'''							)
							# u, v
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =1, 2, -3
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =4, -2, 5
							print(F'''u is {u}'''							)
							print(F'''v is {v}'''							)
							print(F'''uv^T is {u * v.transpose()}'''							)
							# Sherman Morrison
							print(F'''(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowerCAmelCase  ,       __lowerCAmelCase							)}'''							)





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							import doctest

							doctest.testmod()





	testa()


